.TH std::inclusive_scan 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::inclusive_scan \- std::inclusive_scan

.SH Synopsis
   Defined in header <numeric>
   template< class InputIt, class OutputIt >
                                                                \fI(since C++17)\fP
   OutputIt inclusive_scan( InputIt first, InputIt last,    \fB(1)\fP (constexpr since C++20)

                            OutputIt d_first );
   template< class ExecutionPolicy,

             class ForwardIt1, class ForwardIt2 >
   ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,     \fB(2)\fP \fI(since C++17)\fP
                              ForwardIt1 first, ForwardIt1
   last,

                              ForwardIt2 d_first );
   template< class InputIt, class OutputIt, class BinaryOp
   >
                                                                \fI(since C++17)\fP
   OutputIt inclusive_scan( InputIt first, InputIt last,    \fB(3)\fP (constexpr since C++20)

                            OutputIt d_first, BinaryOp op
   );
   template< class ExecutionPolicy,

             class ForwardIt1, class ForwardIt2, class
   BinaryOp >
   ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,     \fB(4)\fP \fI(since C++17)\fP
                              ForwardIt1 first, ForwardIt1
   last,

                              ForwardIt2 d_first, BinaryOp
   op );
   template< class InputIt, class OutputIt,

             class BinaryOp, class T >                          \fI(since C++17)\fP
   OutputIt inclusive_scan( InputIt first, InputIt last,    \fB(5)\fP (constexpr since C++20)

                            OutputIt d_first, BinaryOp op,
   T init );
   template< class ExecutionPolicy,

             class ForwardIt1, class ForwardIt2,
             class BinaryOp, class T >
   ForwardIt2 inclusive_scan( ExecutionPolicy&& policy,     \fB(6)\fP \fI(since C++17)\fP
                              ForwardIt1 first, ForwardIt1
   last,

                              ForwardIt2 d_first, BinaryOp
   op, T init );

   1) Equivalent to inclusive_scan(first, last, d_first, std::plus<>().
   3) Computes the inclusive prefix sum using op.
   For each integer i in [0, std::distance(first, last)), performs the following
   operations in order:
    1. Creates a sequence which is formed by the elements of [first, iter] in order,
       where iter is the next i
       th iterator of first.
    2. Computes the generalized noncommutative sum of the sequence over op.
    3. Assigns the result to *dest, where dest is the next i
       th iterator of d_first.
   5) Same as \fB(3)\fP, but each sequence created is formed by init followed by the elements
   of [first, iter] in order.
   2,4,6) Same as (1,3,5), but executed according to policy.
   These overloads participate in overload resolution only if

   std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true.        (until
                                                                             C++20)
   std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. (since
                                                                             C++20)

   The generalized, noncommutative sum of a sequence of elements over a binary
   operation binary_op is defined as follows:

     * If the sequence only has one element, the sum is the value of the element.
     * Otherwise, performs the following operations in order:
    1. Selects any two adjacent elements elem1 and elem2 from the sequence.
    2. Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence
       with the result.
    3. Repeats steps 1 and 2 until there is only one element in the sequence.

   Given binary_op as the actual binary operation:

     * The result is non-deterministic if the binary_op is not associative (such as
       floating-point addition).
     * For overloads (1-4), if binary_op(*first, *first) is not convertible to the
       value type of decltype(first), the program is ill-formed.
     * For overloads (5,6), if any of the following values is not convertible to T, the
       program is ill-formed:

     * binary_op(init, *first)
     * binary_op(init, init)
     * binary_op(*first, *first)
     * If any of the following conditions is satisfied, the behavior is undefined:

     * For overloads (1-4), the value type of decltype(first) is not MoveConstructible.
     * For overloads (5,6), T is not MoveConstructible.
     * binary_op modifies any element of [first, last).
     * binary_op invalidates any iterator or subrange of [first, last].

.SH Parameters

   first, last - the range of elements to sum
   d_first     - the beginning of the destination range; may be equal to first
   policy      - the execution policy to use. See execution policy for details.
   init        - the initial value
                 binary FunctionObject that will be applied in to the result of
   op          - dereferencing the input iterators, the results of other op, and init
                 (if provided)
.SH Type requirements
   -
   InputIt must meet the requirements of LegacyInputIterator.
   -
   OutputIt must meet the requirements of LegacyOutputIterator.
   -
   ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.

.SH Return value

   Iterator to the element past the last element written.

.SH Complexity

   Given \\(\\scriptsize N\\)N as std::distance(first, last):

   1,2) \\(\\scriptsize O(N)\\)O(N) applications of std::plus<>().
   3-6) \\(\\scriptsize O(N)\\)O(N) applications of op.

.SH Exceptions

   The overloads with a template parameter named ExecutionPolicy report errors as
   follows:

     * If execution of a function invoked as part of the algorithm throws an exception
       and ExecutionPolicy is one of the standard policies, std::terminate is called.
       For any other ExecutionPolicy, the behavior is implementation-defined.
     * If the algorithm fails to allocate memory, std::bad_alloc is thrown.

.SH Example


// Run this code

 #include <functional>
 #include <iostream>
 #include <iterator>
 #include <numeric>
 #include <vector>

 int main()
 {
     std::vector data{3, 1, 4, 1, 5, 9, 2, 6};

     std::cout << "Exclusive sum: ";
     std::exclusive_scan(data.begin(), data.end(),
                         std::ostream_iterator<int>(std::cout, " "),
                         0);

     std::cout << "\\nInclusive sum: ";
     std::inclusive_scan(data.begin(), data.end(),
                         std::ostream_iterator<int>(std::cout, " "));

     std::cout << "\\n\\nExclusive product: ";
     std::exclusive_scan(data.begin(), data.end(),
                         std::ostream_iterator<int>(std::cout, " "),
                         1, std::multiplies<>{});

     std::cout << "\\nInclusive product: ";
     std::inclusive_scan(data.begin(), data.end(),
                         std::ostream_iterator<int>(std::cout, " "),
                         std::multiplies<>{});
 }

.SH Output:

 Exclusive sum: 0 3 4 8 9 14 23 25
 Inclusive sum: 3 4 8 9 14 23 25 31

 Exclusive product: 1 3 3 12 12 60 540 1080
 Inclusive product: 3 3 12 12 60 540 1080 6480

.SH See also

                            computes the differences between adjacent elements in a
   adjacent_difference      range
                            \fI(function template)\fP
   accumulate               sums up or folds a range of elements
                            \fI(function template)\fP
   partial_sum              computes the partial sum of a range of elements
                            \fI(function template)\fP
   transform_inclusive_scan applies an invocable, then calculates inclusive scan
   \fI(C++17)\fP                  \fI(function template)\fP
   exclusive_scan           similar to std::partial_sum, excludes the i^th input
   \fI(C++17)\fP                  element from the i^th sum
                            \fI(function template)\fP
